Convergence Acceleration of Navier-Stokes Equation using Adaptive Wavelet Method

Abstract

The numerical solution of problems with localized structures or sharp transition on uniform grids is impractical, since high-resolution computations are required only in regions where sharp transitions occur. In order to solve these problems computationally in an efficient way, the computational grid should adapt dynamically in time to reflect local changes in the solution. An adaptive wavelet based method enable us an alternate solution to refine grid according to local demands of physical solution. In this study one of such efficient adaptive wavelet method is proposed for convergence acceleration of Navier-Stokes equation. The method is based on Sparse Point Representation which uses only those function values retained after thresholding. The flux evaluation is carried out only at points included in dataset, which results in reducing the necessary computational effort and memory requirements. The numerical results of the adaptive wavelet method are compared with the conventional solver to assess enhancement in computational efficiency.